Simplify 8x^3 square root of 3x+2 square root of 108x^7

$8 x^{3} \sqrt{3 x} + 2 \sqrt{108 x^{7}}$

Simplify each term.

Rewrite $108 x^{7}$ as ${(6 x^{3})}^{2} \cdot (3 x)$ .

Factor $36$ out of $108$ .

$8 x^{3} \sqrt{3 x} + 2 \sqrt{36 (3) x^{7}}$

Rewrite $36$ as $6^{2}$ .

$8 x^{3} \sqrt{3 x} + 2 \sqrt{6^{2} \cdot 3 x^{7}}$

Factor out $x^{6}$ .

$8 x^{3} \sqrt{3 x} + 2 \sqrt{6^{2} \cdot 3 (x^{6} x)}$

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$8 x^{3} \sqrt{3 x} + 2 \sqrt{6^{2} \cdot 3 ({(x^{3})}^{2} x)}$

Move $3$ .

$8 x^{3} \sqrt{3 x} + 2 \sqrt{6^{2} {(x^{3})}^{2} \cdot 3 x}$

Rewrite $6^{2} {(x^{3})}^{2}$ as ${(6 x^{3})}^{2}$ .

$8 x^{3} \sqrt{3 x} + 2 \sqrt{{(6 x^{3})}^{2} \cdot 3 x}$

Add parentheses.

$8 x^{3} \sqrt{3 x} + 2 \sqrt{{(6 x^{3})}^{2} \cdot (3 x)}$

Pull terms out from under the radical.

$8 x^{3} \sqrt{3 x} + 2 (6 x^{3} \sqrt{3 x})$

Multiply $6$ by $2$ .

$8 x^{3} \sqrt{3 x} + 12 x^{3} \sqrt{3 x}$

Add $8 x^{3} \sqrt{3 x}$ and $12 x^{3} \sqrt{3 x}$ .

$20 x^{3} \sqrt{3 x}$